Question

the length and breadth of a rectangle are represented by (3x¹⁰y⁵)‐² and (5x‐⁷y⁹)‐¹ find the expression which represents the area of the rectangle ​

Answer 1

Answer:

(i) Let us first factorize the given expression 25a

2

−35a+12 as shown below:

25a

2

−35a+12

=25a

2

−15a−20a+12

=5a(5a−3)−4(5a−3)

=(5a−4)(5a−3)

Therefore, the area of the rectangle is (5a−4)(5a−3) and we also know that the area of the rectangle is A=length×breadth.

Hence, the length and breadth can both be (5a−4) or (5a−3).

(ii) Let us first factorize the given expression 24x

2

−15x as shown below:

24x

2

−15x

=x(24x−15)

Therefore, the area of the rectangle is x(24x−15) and we also know that the area of the rectangle is A=length×breadth.

Hence, the length and breadth can both be x or (24x−15).

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